The Quasi-geostrophic (QG) Omega Equation represents a method for diagnosing mid-latitude synoptic-scale vertical motion at a specified time. In the absence of diabatic processes, it implies that vertical motion can be calculated from a series of geopotential height analyses at different pressure levels. It is a powerful conceptual tool for meteorologists because its terms are straightforward to estimate qualitatively and physically. With practice, the conclusions can be applied to real-time thickness, geopotential height, vorticity, or temperature analyses.
QG Omega Equation Description
The adiabatic form of the QG Omega Equation (QGOE) is presented below:
The left-hand side (LHS) term is similar to the 3-D laplacian of omega. It is commonly assumed that the dominant mode of vertical motion is sinusoidal: approximately zero at both the surface and tropopause, and attaining a maximum/minimum value in the mid-troposphere. Under these circumstances, the LHS differential operator behaves qualitatively like a negative sign.
The first right-hand side (RHS) term represents differential geostrophic absolute vorticity advection.
The second RHS term is proportional to the horizontal laplacian of horizontal geostrophic thickness advection (which can be interpreted as thermal advection).
The omega equation is of diagnostic use only. It reveals the omega distribution at the time of a specified geopotential height analysis. However, as there are no time derivatives, it does not predict future vertical motion.
QG Omega Widget Description
This tool evaluates the omega field associated with a simple two-level model of the troposphere in midlatitudes. The method of calculations can be found in T.N. Carlson's "Mid-Latitude Weather Systems" on pages 268-275 or in J. Holton's "An Introduction to Dynamic Meteorology" on pages 166-170.
The 1000hPa height distribution is specified and is sinusoidal in x and y. This represents an idealised wave-train of circular high and low pressure systems, with wavelength of 4000km.
The thermal distribution is represented by the 1000-500hPa thickness, where the direction of isotherms is assumed to be constant with height. The user can specify either a zonal thickness pattern, or a sinusoidal thickness pattern whose position relative to the 1000hPa pattern can be varied.
The 500 hPa height distribution is determined from the 1000hPa height and 1000-500hPa thickness.
The omega distribution is presented at 500hPa. The omega pattern will intensify or weaken based on the thickness pattern and phase chosen by the user.
These levels were chosen so that forecasters could conceptualize actual omega distributions on the basis of a quick inspection of MSLP/Thickness or 500hPa Geopotential Height/Temperature charts.
The impact of the RHS forcing terms can be visualized separately and overlaid to assess their contribution to the total vertical motion.
The omega distribution will change depending upon the offset of the 500hPa and thickness fields that is selected by the user.
Explore the relationship between 500hPa heights, 1000-500hPa thickness and their relation to omega by changing the phase and pattern settings at the upper left of the widget. Understand the results by viewing the variables listed in the right-hand menu. Click below for full step-by-step instructions or to go directly to the widget.